What I also noted was that occasionally Sid Caesar would perform (usually with Carl Reiner, who was both an actor and writer on the show) the old sketch they were talking about. Here's an example of that.
The first writer you'll see is Danny Simon, older brother of Neil. They were writing partners at the time. Danny is also the real-life model for the messy character Oscar Madison in The Odd Couple. At one point in the video you'll also see a three-shot of Larry Gelbart, Mel Brooks and Neil Simon. Folks, three-shots don't get much better than that... But then, the entire panel was amazing.